EE 5340 Semiconductor Device Theory Lecture 01 – Spring 2011 Professor Ronald L. Carter

©rlc L01 18Jan20112 Web Pages *Review the following R. L. Carter’s web page – EE 5340 web page and syllabus – University and College Ethics Policies – –

©rlc L01 18Jan20113 First Assignment Send to –On the subject line, put “5340 ” –In the body of message include address: ______________________ Your Name*: _______________________ Last four digits of your Student ID: _____ * Your name as it appears in the UTA Record - no more, no less

©rlc L01 18Jan20114 Quantum Concepts Bohr Atom Light Quanta (particle-like waves) Wave-like properties of particles Wave-Particle Duality

©rlc L01 18Jan20115 Bohr model for Hydrogen atom Electron (-q) rev. around proton (+q) Coulomb force, F = q 2 /4  o r 2, q = 1.6E-19 Coul,  o =8.854E-14Fd/cm Quantization L = mvr = nh/2 , h =6.625E-34J-sec

©rlc L01 18Jan20116 Bohr model for the H atom (cont.) E n = -(mq 4 )/[8  o 2 h 2 n 2 ] ~ eV/n 2 r n = [n 2  o h 2 ]/[  mq 2 ] ~ 0.05 nm = 1/2 A o for n=1, ground state

©rlc L01 18Jan20117 Bohr model for the H atom (cont.) E n = - (mq 4 )/[8  o 2 h 2 n 2 ] ~ eV/n 2 * r n = [n 2  o h 2 ]/[  mq 2 ] ~ 0.05 nm = 1/2 A o * *for n=1, ground state

©rlc L01 18Jan20118 Energy Quanta for Light Photoelectric Effect: T max is the energy of the electron emitted from a material surface when light of frequency f is incident. f o, frequency for zero KE, mat’l spec. h is Planck’s (a universal) constant h = 6.625E-34 J-sec

©rlc L01 18Jan20119 Photon: A particle -like wave E = hf, the quantum of energy for light. (PE effect & black body rad.) f = c/, c = 3E8m/sec, = wavelength From Poynting’s theorem (em waves), momentum density = energy density/c Postulate a Photon “momentum” p = h/  = hk, h = h/2  wavenumber, k =  2  /

©rlc L01 18Jan Wave-particle duality Compton showed  p = hk initial - hk final, so an photon (wave) is particle-like

©rlc L01 18Jan Wave-particle duality DeBroglie hypothesized a particle could be wave-like,  = h/p

©rlc L01 18Jan Wave-particle duality Davisson and Germer demonstrated wave-like interference phenomena for electrons to complete the duality model

©rlc L01 18Jan Newtonian Mechanics Kinetic energy, KE = mv 2 /2 = p 2 /2m Conservation of Energy Theorem Momentum, p = mv Conservation of Momentum Thm Newton’s second Law F = ma = m dv/dt = m d 2 x/dt 2

©rlc L01 18Jan Quantum Mechanics Schrodinger’s wave equation developed to maintain consistence with wave-particle duality and other “quantum” effects Position, mass, etc. of a particle replaced by a “wave function”,  (x,t) Prob. density = |  (x,t)   (x,t)|

©rlc L01 18Jan Schrodinger Equation Separation of variables gives  (x,t) =  (x)  (t) The time-independent part of the Schrodinger equation for a single particle with Total E = E and PE = V. The Kinetic Energy, KE = E - V

©rlc L01 18Jan Solutions for the Schrodinger Equation Solutions of the form of  (x) = A exp(jKx) + B exp (-jKx) K = [8  2 m(E-V)/h 2 ] 1/2 Subj. to boundary conds. and norm.  (x) is finite, single-valued, conts. d  (x)/dx is finite, s-v, and conts.

©rlc L01 18Jan Infinite Potential Well V = 0, 0 < x < a V --> inf. for x a Assume E is finite, so  (x) = 0 outside of well

©rlc L01 18Jan References *Fundamentals of Semiconductor Theory and Device Physics, by Shyh Wang, Prentice Hall, **Semiconductor Physics & Devices, by Donald A. Neamen, 2nd ed., Irwin, Chicago.